arXiv subjects

Yen-Kheng Lim

Publications and source records attributed to Yen-Kheng Lim.

At least 37 records · Page 2Linked to original sources

arXiv2021

Light-ring pairs from $A$-discriminantal varieties

When geodesic equations are formulated in terms of an effective potential $U$, circular orbits are characterised by $U=\partial_a U=0$. In this paper we consider the case where $U$ is an algebraic function. Then the condition for circular orbits defines an $A$-discriminantal variety. A theorem by Rojas and Rusek, suitably interpreted in the context of effective potentials, gives a precise criteria for certain types of spacetimes to contain at most two branches of light rings (null circular orbits), where one is stable and the other one unstable. We identify a few classes of static, spherically-symmetric spacetimes for which these two branches occur and show that the spacetimes with non-degenerate horizons do not have stable light rings.

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arXiv2021

Motion of charged particles around a magnetic black hole/topological star with a compact extra dimension

We study the motion of charged particles in a family of five-dimensional solutions describing either a black hole or topological star with a fifth compact dimension stabilised by a magnetic flux. The particle's trajectory is shown to move along the surface of a Poincaré cone. The radial motion shows a rich structure where the existence of various bound, plunging, or escaping trajectories depend on the constants of motion. Curves of energy and angular momentum corresponding to spherical orbits show a swallow-tail structure highly reminiscent to phase transitions of thermodynamics. When the momentum along the compact direction is varied, the is a critical point beyond which the swallow-tail kink disappears and becomes a smooth curve.

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arXiv2021

Null geodesics in the C-metric with cosmological constant

In this paper we study the motion of photons or massless particles in the C-metric with cosmological constant. The Hamilton--Jacobi equations are known to be completely separable, giving a Carter-like quantity $Q$ which is a constant of motion. All possible trajectories are classified according to a two-dimensional parameter space representing the particle's angular momentum and energy scaled in units of $Q$. Exact solutions are given in the C-metric coordinates in terms of Jacobi elliptic functions. Using the exact solutions, we find examples of periodic orbits on the photon surface.

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arXiv2020

Orbital mechanics and quasiperiodic oscillation resonances of black holes in Einstein-Æther theory

In this paper, we study the motion of test particles around two exact charged black-hole solutions in Einstein-Æther theory. Specifically, we first consider the quasi-periodic oscillations (QPOs) and their resonances generated by the particle moving in the Einstein-Æther black hole and then turn to study the periodic orbits of the massive particles. For QPOs, we drop the usually adopted assumptions $ν_U=ν_θ$, $ν_L=ν_r$, and $ν_U/ν_L=3/2$ with $ν_U$ ($ν_L$) and $ν_r$ ($ν_θ$) being the upper (lower) frequency of QPOs and radial (vertical) epicyclic frequency of the orbiting particles, respectively. Instead, we put-forward a new working ansatz for which the Keplerian radius is much closer to that of the innermost stable circular orbit and explore in detail the effects of the æther field on the frequencies of QPOs. We then realize good curves for the frequencies of QPOs, which fit to data of three microquasars very well by ignoring any effects of rotation and magnetic fields. The innermost stable circular orbits (isco) of timelike particles are also analyzed and we find the isco radius increases with increasing $c_{13}$ for the first type black hole while decreases with increasing $c_{14}$ for the second one. We also obtain several periodic orbits and find that they share similar taxonomy schemes as the periodic equatorial orbits in the Schwarzschild/Kerr metrics, in addition to exact solutions for certain choices of the Einstein-Æther parameters. The equations for null geodesics are also briefly considered, where we study circular photon orbits and bending angles for gravitational lensing.

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arXiv2020

Hypocycloid motion in the Melvin magnetic universe

The trajectory of a charged test particle in the Melvin magnetic universe is shown to take the form of hypocycloids in two different regimes, first of which is the class of perturbed circular orbits, and secondly in the weak-field approximation. In the latter case we find a simple relation between the charge of the particle and the number of cusps. These two regimes are within a continuously connected family of deformed hypocycloid-like orbits parametrised by the magnetic flux strength of the Melvin spacetime.

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arXiv2020

Charged dilaton black hole with multiple Liouville potentials and gauge fields

A solution to an Einstein--Maxwell--dilaton-type theory with $M$ Liouville potentials and $N$ gauge fields is presented, where $M$ and $N$ are arbitrary integers. This exact solution interpolates between the Lifshitz black hole and the topological dilaton black hole. The thermodynamic behaviour of the solution is found to be similar to that of the Lifshitz black hole, where a phase transition may occur for sufficiently small charge in the canonical ensemble, or sufficiently small potential in the grand canonical ensemble.

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arXiv2019

Rotation curves and orbits in the scalar field dark matter halo spacetime

The spacetime satisfying the flat curve condition for galaxies is shown to be the zero mass limit of the dilaton blackhole with an exponential potential. We derive the geodesic equations and by studying rotational curves and light deflection, and find that the presence of the dilaton increases the gravitational effects overall but diminishes the contribution from the central mass when the distances are close to the black hole. Also, the dilaton reduces the size of innermost stable circular time-like orbits, while the radius of the photon sphere may be larger or smaller than its Schwrazschild counterpart, depending on the strength of the dilaton field. We also show that a generalisation of the flat-curve-condition spacetime considered elsewhere in the literature does not solve the Einstein equation.

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arXiv2018

Field equations and particle motion in covariant emergent gravity

We derive the full set of field equations based on Hossenfelder's recent covariant formulation of the emergent gravity model, along with perturbative and exact solutions. The exact solution describes a static, spherically-symmetric spacetime with a non-trivial vector field which plays the role of dark matter under the emergent gravity paradigm. Equations of motion of relativistic test masses are derived and are shown to reduce to Modified Newtonian Dynamics with additional relativistic corrections. It is also shown that the presence of the vector field gives an additional positive contribution to the bending angle in the deflection of light.

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arXiv2018

Electric/magnetic universe with a cosmological constant

A spacetime consisting of parallel electric/magnetic fields held together by its own gravity in the presence of a cosmological constant $Λ$ is derived as a limit of the de Sitter/anti-de Sitter C-metric. The limiting procedure is similar to the $Λ=0$ case where the Melvin universe is derived from the C-metric. Under an appropriate coordinate transformation, we show that this solution is equivalent to the solution obtained by Astorino. Some physical and geometrical properties of the solution are studied, as well as its geodesics. For $Λ<0$, the solution is asymptotically locally anti-de Sitter, and can be derived as a double-Wick rotation of a charged anti-de Sitter black hole with a planar horizon.

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arXiv2018

Criteria of existence for bounce solutions in false vacuum decay with gravity

The bounce solutions of self-interacting scalar fields coupled to gravity are studied using a semi-classical approach. We found that bounce solutions have a maximum required barrier curvature, in addition to the known minimum required barrier curvature. In particular, as the maximum barrier curvature is approached, the scale factor of the well-known Colemen-De Luccia (CDL) bounce solutions become divergent. Unlike the CDL or its more general oscillating bounce counterparts, this cannot be considered as a subset of the Hawking-Turok solution.

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arXiv2017

Kasner-type singularities and solitons with Lifshitz asymptotics

We present an exact solution in Einstein-Maxwell-dilaton gravity describing a spacetime with an anisotropic Kasner-type singularity and Lifshitz asymptotics. This configuration can also be supported by a phantom scalar while still satisfying the Null Energy Condition. For certain parameters of this solution, null geodesics can have an infinitely deep effective potential, thus trapping photons in a finite region along the radial direction. Some examples of periodic null geodesics are obtained. A particularly interesting special case of this solution is a regular, soliton-type metric that retains its Lifshitz scaling in the time coordinate.

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arXiv2017

Periodic orbits around a spherically symmetric naked singularity

The motion of time-like test particles in the Fisher/Janis-Newman-Winicour (F/JNW) spacetime is studied with the Hamiltonian formulation of the geodesic equations. The spacetime is characterised by its mass parameter $r_g$ and scalar field parameter $ν$. The innermost bound and stable circular orbits are calculated and the effective potential is analysed. Consistent with numerical results in earlier literature, for $ν<1/2$, particles with non-zero angular momentum encounter an infinite potential barrier, preventing them from reaching the naked singularity at $r=r_g$. Periodic orbits in the spacetime are also obtained. Compared to the periodic orbits around the Schwarzschild black hole, it is found that typically lower energies are required for the same orbits in the F/JNW spacetime.

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arXiv2017

Cohomogeneity-1 solutions in Einstein-Maxwell-dilaton gravity

The field equations for Einstein-Maxwell-dilaton gravity in $D$ dimensions are reduced to an effective one-dimensional system under the influence of exponential potentials. Various cases where exact solutions can be found are explored. With this procedure, we present interesting solutions such as a one-parameter generalisation of the dilaton-Melvin spacetime and a three-parameter solution that interpolates between the Reissner-Nordström and Bertotti-Robinson solution. This procedure also allows simple, alternative derivations of known solutions such as the Lifshitz spacetime and the planar Anti-de Sitter naked singularity. In the latter case, the metric is cast in a simpler form which reveals the presence of an additional curvature singularity.

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arXiv2017

Exact gravitational lensing in conformal gravity and Schwarzschild-de Sitter spacetime

An exact solution is obtained for the gravitational bending of light in static, spherically symmetric metrics which includes the Schwarzschild-de Sitter spacetime and also the Mannheim-Kazanas metric of conformal Weyl gravity. From the exact solution, we obtain a small bending-angle-approximation for a lens system where the source, lens and observer are co-aligned. This expansion improves previous calculations where we systematically avoid parameter ranges that correspond to non-existent null trajectories. The linear coefficient $γ$ characteristic to conformal gravity is shown to contribute enhanced deflection compared to the angle predicted by General Relativity for small $γ$.

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arXiv2016

Charged C-metric in conformal gravity

Using a C-metric-type ansatz, we obtain an exact solution to conformal gravity coupled to a Maxwell electromagnetic field. The solution resembles a C-metric spacetime carrying an electromagnetic charge. The metric is cast in a factorised form which allows us to study the domain structure of its static coordinate regions. This metric reduces to the well-known Mannheim-Kazanas metric under an appropriate limiting procedure, and also reduces to the (Anti-)de Sitter C-metric of Einstein gravity for a particular choice of parameters.

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arXiv2015

Dynamics of a charged particle around a weakly magnetized naked singularity

We examine the motion of a charged particle in the vicinity of a weakly magnetized naked singularity. The escape velocity and energy of the particle moving around the naked singularity after being kicked by another particle or photon are investigated. Also at the innermost stable circular orbit (ISCO) escape velocity and energy are examined. Effective potential and angular momentum of the particle are also discussed. We discuss the center of mass energy after collision between two particles having same mass and opposite charges moving along the same circular orbit in the opposite direction. It is investigated that under what conditions maximum energy can be produced as a result of collision.

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arXiv2015

Deformed hyperbolic black holes

Black holes with planar or hyperbolic horizons are known to exist in AdS space, alongside the usual ones with spherical horizons. In this paper, we consider a one-parameter generalisation of these black holes that is contained in the AdS C-metric. In terms of the domain-structure analysis recently developed for such solutions, these black holes have a domain in the shape of a triangle. It is shown that the horizons of these black holes are deformed hyperbolic spaces, with the new parameter controlling the amount of deformation. The space-times are static and completely regular outside the horizons. We argue that these black holes are hyperbolic analogues of the "slowly accelerating" spherical black holes known to exist in AdS space.

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arXiv2015

A new form of the C-metric with cosmological constant

The new form of the C-metric proposed by Hong and Teo, in which the two structure functions are factorised, has proved useful in its analysis. In this paper, we extend this form to the case when a cosmological constant is present. The new form of this solution has two structure functions which are partially factorised; moreover, the roots of the structure functions are now regarded as fundamental parameters. This leads to a natural representation of the solution in terms of its so-called domain structure, in which the allowed coordinate range can be visualised as a "box" in a two-dimensional plot. The solution is then completely parameterised by the locations of the edges of this box, at least in the uncharged case. We also briefly analyse other possible domain structures---in the shape of a triangle and trapezoid---that might describe physically interesting space-times within the AdS C-metric.

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